We analyze in detail the discrete-time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position...

We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known quantum kicked rotor, this model can be mapped into a...

We report an enhancement of the decay rate of the survival probability when non-local initial conditions in position space are considered in the quantum walk on the line. It is shown how this interference effect can be understood analytically by using previously derived results. Within a...

We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical diffusive behavior. In the case of measurements, we show...

We consider the effect of different unitary noise mechanisms on the evolution of a quantum walk (QW) on a linear chain with a generic coin operation: (i) bit-flip channel noise, restricted to the coin subspace of the QW and (ii) topological noise caused by randomly broken links in the linear...

Iterated bipartite quantum games are implemented in terms of the discrete-time quantum walk on the line. Our proposal allows for conditional strategies, as two rational agents make a choice from a restricted set of two-qubit unitary operations. We discuss how several classical strategies are...

We analyze the responses of a quantum search algorithm to an external monochromatic field and to the decoherences introduced through measurement processes. The external field in general affects the functioning of the search algorithm. However, depending on the values of the field parameters,...

In this work we use the wave equation to obtain a classical analogue of the quantum search algorithm and we verify that the essence of search algorithms resides in the establishment of resonances between the initial and the searched states. In particular we show that, within a set of N vibration...

We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to N, where N is the database size. This search algorithm can be implemented using any Hamiltonian with a discrete energy spectrum through...

Using information theory, a new variational principle for incompressible fluids is derived. This principle is similar to a known plasma stability criterion which has successfully been applied to study the stability of different steady flows. Its main advantages, when compared to traditional...